This invention relates to the production of oil and gas from a subsea fixture such as an oil well drilled in the bottom of a body of water. It relates especially to a floating production system over such subsea wells wherein flexible riser pipes are connected to the subsea well or subsea pipeline and the other end of the riser pipes are supported at the surface of the body of water by a floating vessel or buoy where it is then conducted to a floating vessel or tanker. In some cases, an underwater buoy is anchored so that the buoy is at an intermediate distance between the surface of the body of water and the bottom, e.g., one-half of the distance. This underwater buoy is provided with a cradle over which the flexible riser passes as supported. One problem with the prior risers and underwater buoy system is that the currents cause the underwater buoys to twist and rotate to the extent that the riser pipes may be damaged to the point where they may rupture.